The Domeyko Cordillera, the westernmost uplifted crustal block of the composite High Andes of northern Chile (20 degrees S to 28 degrees S) hosts a narrow N-S trending belt of Late Eocene-Oligocene giant porphyry copper deposits, which include Collahuasi, Chuquicamata, El Abra, La Escondida, and El Salvador. These deposits are spatially and genetically associated with the closing igneous activity along this range, prior to a 30 km eastward jump of the magmatic front in response to tectonic plate interaction. The porphyry copper deposits are also spatially associated with a major intraarc strike-slip shear system, the Domeyko Fault System. Although the tectonic uplift of the 3000 m to 5000 m high range has generally been assumed to be mostly Miocene in age, field relationships suggest that the Domeyko Fault System and tectonic uplift were active as early as the Eocene, coinciding with porphyry copper emplacement between 41 Ma and 30 Ma. Apatite fission track (FT) thermochronology provides both age data and a time-temperature history for rocks since they cooled below a temperature of ca. 125 degrees C (equivalent to a depth of 4 km to 5 km under normal geothermal gradients) on their way to the surface during exhumation, or after a heating event. Apatite FT data from the Paleozoic crystalline basement of the Domeyko Cordillera indicate that at least 4 km to 5 km of rocks were eroded during exhumation of this tectonic block between ca. 50 Ma to 30 Ma (Middle Eocene to Early Oligocene), a time that immediately precedes and overlaps with the emplacement of giant porphyry copper deposits. The FT data constrain the age and duration of a period of crustal thickening and extensive erosion known as the Incaic compression, an event recognized in the Andes of Chile and Peru. Assuming that cooling was due to denudation alone, modelling of the FT data allow estimation of denudation rates between 200 and 100 m/My during this period. In contrast, exposures of pre-porphyry Paleocene intrusives on the western edge of the Domeyko Cordillera reveal apatite FT ages that are concordant with biotite 40 Ar- 39 Ar dates, indicating shallow emplacement, fast cooling and negligible exhumation. The apatite FT ages of the Chuquicamata and El Abra porphyry copper deposits are only marginally younger than their 40 Ar- 39 Ar dates, implying fast cooling/exhumation of shallow mineralizing systems (ca. 2 km to 3 km). Their FT time-temperature history is compatible with extremely low rates of exhumation (ca. 50 m/My) since about 30 Ma (Early Oligocene). This limited extent of erosion, due to exceptional aridity, has greatly contributed to the preservation of rich supergene enriched blankets above some of the porphyry copper deposits. A model is proposed, which is consistent with field relationships, geochemical, and geochronological data. High relative velocities and intermediate-angle oblique convergence between the Nazca and South American plates in the Eocene-Early Oligocene led to intra-arc transpression partitioned into reverse faults of opposing vergence and a right-lateral shear system (the Domeyko Shear System) localized along the magmatic front. Crustal shortening and thickening led to uplift within the Domeyko Fault System and to erosion of at least 4 km to 5 km. Crustal thickening deepened the zone of magma generation, and magmas accumulated in the lower crust, allowing small volumes to rise rapidly to shallow levels along transtensional domains of the regional shear system. A similar model of crustal thickening and shortening before and during porphyry copper emplacement in zones of transtension may also apply to the Miocene-Pliocene giant porphyry copper province of central Chile.